Weird outline between two roughness values
I could be wrong, but I think the halo is caused by the very same phenomenon as the inversion, that it can be  expected, and it's made more obvious by the low resolution of the roughness map.

Let's divide the material into three regions for the sake of argument: glossy, semi-glossy, and rough.

Where the glossy is directly reflecting a dark backgound, the rough is lighter: it's reflecting contributions from many more directions, including the lighter areas.

Where the glossy is directly reflecting a light background,  like the sky, the rough is darker - its contributions include scattered reflections from the ground.

In the grey zone, around the inversion, it's possible for the semi-glossy to be brighter than both the glossy and the rough: imagine the cone from which reflection-samples are being taken. It's possible for the medium cone to contain a bigger fraction of light areas than both the narrow and the wide, especially if there is variation along the horizon. The semi-glossy area is particularly prominent in your texture-map - all of the anti-aliased region between light and dark.

Maybe not strictly part of the problem, but there's also an optical illusion going on, like the checker-shadow illusion illustrated here. The 'dark' areas near the top of your rough regions of grain are actually lighter than the 'light' areas toward the bottom, although they don't look it.

You might consider playing with a procedural wood using something like this method.



.. which can get the same inversion, but with a less prominent, distinct, middle-zone. The material shown above is in this .blend, and can be tweaked.